Extraction of Generalized Parton Distribution Observables from Deeply Virtual Electron Proton Scattering Experiments

We provide the general expression of the cross section for exclusive deeply virtual photon electroproduction from a spin 1/2 target using current parameterizations of the off-forward correlation function in a nucleon for different beam and target polarization configurations up to twist three accuracy. All contributions to the cross section including deeply virtual Compton scattering, the Bethe-Heitler process, and their interference, are described within a helicity amplitude based framework which is also relativistically covariant and readily applicable to both the laboratory frame and in a collider kinematic setting. Our formalism renders a clear physical interpretation of the various components of the cross section by making a connection with the known characteristic structure of the electron scattering coincidence reactions. In particular, we focus on the total angular momentum, $J_z$, and on the orbital angular momentum, $L_z$. On one side, we uncover an avenue to a precise extraction of $J_z$, given by the combination of generalized parton distributions, $H+E$, through a generalization of the Rosenbluth separation method used in elastic electron proton scattering. On the other, we single out for the first time, the twist three angular modulations of the cross section that are sensitive to $L_z$. The proposed generalized Rosenbluth technique adds an important constraint for mapping the 3D structure of the nucleon.